Reynolds Number Dependence for Laminar Flow Loss Coefficients in Tee and Wye Junctions

Abstract

In fluid flow piping systems, tee and wye junctions are commonly encountered and the study of flow through them has been well documented. Most of these studies have focused on flow characterized as turbulent for which there are nearly constant losses in pressure and kinetic energy in the junctions. Laminar flow has received much less attention since it is not frequently observed in macro scale piping systems where pipe diameters are measured in centimeters. The recent increase in use of micro scale flow devices calls for more research into laminar flow behavior that dictates the design and operation of these devices. This paper documents results from computational fluid dynamics (CFD) simulations of flow in planar tee and wye junctions. The junctions studied consisted of circular pipes with two outlets and one inlet. The angles between the tee and wye junctions were fixed to 180 and 60 degrees, respectively. The inlet pipe diameter was fixed at 50 microns and the outlet pipe diameters were chosen to satisfy the continuity equation constrained to have equal velocities in all pipes. The lengths of the inlet and outlet pipes were varied to achieve fully developed flow within the junction. Following a grid resolution study performed on a sample tee junction, a generalized algorithm was designed and implemented to create three-dimensional models of these junctions subject to the former conditions. In the CFD simulations, Reynolds number was varied in the laminar characterized region between 1 and 2000. The simulations calculated static pressure and velocity magnitude values for a number of planes intersecting the junctions along the inlet and outlet pipes. From these values, pressure and kinetic energy gradients were calculated to estimate the static pressure and kinetic energy at the inlet and outlet pipes of each junction. Finally, these inlet and outlet values were used to calculate the stagnation pressure loss coefficient, which reflects dimensionless losses of pressure and kinetic energy for the junction. These coefficients ranged from 1 to 300 for the tee junction and 1 to 400 for the wye junction over the specified range of Reynolds number. The values were inversely proportional to Reynolds number and curve fits were provided for valid ranges.

A unified method for estimating pressure losses at vascular junctions

“…Kiser et al . reported results of a CFD study that suggested K ∼ 1 for 200 < R e < 2000 (in agreement with our results). However, for R e < 200, an inverse relationship with R e was found, with K reaching 300‐400 at R e = 1.…”

“…The majority of work relating to junction loss coefficients has been devoted to high Re flow, but a few investigators have studied junction losses at low Re, which may be of interest in micro-scale flow devices. Kiser et al [56] reported results of a CFD study that suggested K 1 for 200 < Re < 2000 (in agreement with our results). However, for Re < 200, an inverse relationship with Re was found, with K reaching 300-400 at Re D 1.…”

“…Kiser et al . suggested this large quantitative discrepancy may have been due to differences in the junction geometries employed.…”

“…Kiser et al . did not extrapolate pressure to x = 0 as we did, but calculated Δ p i , j as the difference between pressures at the inlet and outlet of the junction (i.e. at approximately x =±D).…”

“…A similar trend but coefficients at least one order of magnitude greater were reported by Jamison and Villemonte [57] on the basis of tube experiments. Kiser et al [56] suggested this large quantitative discrepancy may have been due to differences in the junction geometries employed. However, we suspect that the large coefficients at low Re reported in both of these studies may be spurious.…”